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December 9, 2009 •F i n a l E x a m R e m i n d e r s : •Date: Monday, December 14, 2009 •Time: 8:00-10:30am •Place: IRC 1 (Here) •What to Bring: Calculator #2 Pencil 2 Pages (double-sided) of notes •M a k e u p L a b - O n O W L , d u e a t f i n a l e x a m •T o d a y •Chapter 10: Gases •F r i d a y •Chapter 11: Intermolecular Forces and the Liquid State (Fri.) Kinetic Molecular Theory & Gases Gas molecules far apart, always in motion, collide with walls of container (pressure) Temperature Average Kinetic Energy Higher temperature = higher average kinetic energy Kinetic energy and velocity are not the same Higher molar mass will move slower at the same temperature Boltzmann distribution Plot of molecular speed (x) vs. number of molecules (y) Shows range of speeds in a collection of molecules Gases- Equations from last time… Kinetic energy of one molecule 1 2 KE mv where m mass , v veloc 2 Average Kinetic energy of many molecules 12 3 KE m v RT 2 2 T temperatur e in Kelvin , 8.3145 J 0.082057 L atm R gas constant mol K K mol Average speed of molecules 3 RT 2 v v 8 . 3415 J / K mol , M mol ma in kg / m rms R M Gas Diffusion Gas Effusion Graham’s Law of Effusion Graham’s Law Example A sample of ethane, C2H6, effuses through a small hole at a rate of 3.6 x 10-6 mol/hr. An unknown gas, under the same conditions, effuses at a rate of 1.3 x 10-6 mol/hr. Calculate the molar mass of the unknown gas. Back to Pressure… Collisions between gas molecules and container exerts a force on container wall More collisions and more energetic collisions = greater force = higher pressure Kinetic molecular theory gives conceptual framework for understanding the behavior of gases P and n P and T (P n) (P T) Today’s Temp: 35°F Pressure Gauge Today’s Temp: 85°F Pressure Gauge Back to Pressure… Collisions between gas molecules and container exerts a force on container wall More collisions and more energetic collisions = greater force = higher pressure Kinetic molecular theory gives conceptual framework for understanding the behavior of gases P and n P and T V and T P and V (P n) (P T) (V 1/T) (P 1/V) Volume of balloon at room temperature Volume of balloon at 5°C The Gas Laws Boyle’s P1V1 P2V2 Ideal Gas Law PV nRT Charles’ V1 V2 T1 T2 Avogadro’s V1 V2 n1 n2 R 0.082057 L atm K mol Using the Gas Laws If you know 3 variables, solve for the fourth If some properties are constant, trends in one property can predict another STP (“Standard Temperature and Pressure”) T= 273 K P= 1 atm Strategy: Take note of the variables you know, find the appropriate equation, then “plug and chug” (or just remember PV=nRT and derive the appropriate equation every time) Examples 1. A gas has a volume of 3L at 2 atm. What is its volume at 4 atm? 2. A gas has a volume of 4.1 L at 127 C. What is its volume at 227? Examples 3. What volume does 7.4 grams of ethane (C2H2) occupy at standard temperature and pressure? 4. The propane tank of a camping stove contains 3,000g of liquid C3H8. How large a container would be needed to hold the same amount of propane as a gas at 25C and 2250mmHg?